Amanda is the owner of a small chain of dental offices. She sent out the yearly satisfaction survey to 600 randomly selected patients and received 544 surveys back. When looking through the results, she noticed that the downtown dental office staff had 84% of clients reporting satisfaction with services, while the uptown dental office staff had 76% of clients reporting satisfaction with services. Which of the following sets shows Amanda's null hypothesis and alternative hypothesis?Null Hypothesis: The proportion of clients satisfied at the downtown office is equal to the proportion of clients satisfied at the uptown office. Alternative Hypothesis: There is a difference in the satisfaction between the uptown and the downtown clients. Null Hypothesis: The proportion of clients satisfied at the downtown office is greater than the proportion of clients satisfied at the uptown office.Alternative Hypothesis: Downtown clients are less satisfied with the dental office staff than uptown clients.Null Hypothesis: The proportion of clients satisfied at the uptown office is 76%.Alternative Hypothesis: There is no difference in the satisfaction between the uptown and the downtown clients.Null Hypothesis: The proportion of clients satisfied at the downtown office is 84%.Alternative Hypothesis: Uptown clients are more satisfied with the dental office staff than downtown clients.
Question
Amanda is the owner of a small chain of dental offices. She sent out the yearly satisfaction survey to 600 randomly selected patients and received 544 surveys back. When looking through the results, she noticed that the downtown dental office staff had 84% of clients reporting satisfaction with services, while the uptown dental office staff had 76% of clients reporting satisfaction with services. Which of the following sets shows Amanda's null hypothesis and alternative hypothesis?Null Hypothesis: The proportion of clients satisfied at the downtown office is equal to the proportion of clients satisfied at the uptown office. Alternative Hypothesis: There is a difference in the satisfaction between the uptown and the downtown clients. Null Hypothesis: The proportion of clients satisfied at the downtown office is greater than the proportion of clients satisfied at the uptown office.Alternative Hypothesis: Downtown clients are less satisfied with the dental office staff than uptown clients.Null Hypothesis: The proportion of clients satisfied at the uptown office is 76%.Alternative Hypothesis: There is no difference in the satisfaction between the uptown and the downtown clients.Null Hypothesis: The proportion of clients satisfied at the downtown office is 84%.Alternative Hypothesis: Uptown clients are more satisfied with the dental office staff than downtown clients.
Solution
The correct set of hypotheses for Amanda's situation would be:
Null Hypothesis: The proportion of clients satisfied at the downtown office is equal to the proportion of clients satisfied at the uptown office.
Alternative Hypothesis: There is a difference in the satisfaction between the uptown and the downtown clients.
This is because the null hypothesis is usually a statement of no effect or no difference and is the assumption that any kind of difference or significance you see in a set of data is due to chance. The alternative hypothesis is what you might believe to be true or hope to prove true.
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